Daniel is 3 times as old as Stephanie. Twelve years ago, Daniel was 7 times as old as Stephanie. How old is Daniel now?
Answer: We can use the given information to write down two equations that describe the ages of Daniel and Stephanie. Let Daniel's current age be $d$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $d = 3s$ Twelve years ago, Daniel was $d - 12$ years old, and Stephanie was $s - 12$ years old. The information in the second sentence can be expressed in the following equation: $d - 12 = 7(s - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $s$ and substitute it into our second equation. Solving our first equation for $s$ , we get: $s = d / 3$ . Substituting this into our second equation, we get: $d - 12 = 7($ $(d / 3)$ $- 12)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 12 = \dfrac{7}{3} d - 84$ Solving for $d$ , we get: $\dfrac{4}{3} d = 72$ $d = \dfrac{3}{4} \cdot 72 = 54$.